Tax reforms and the underground economy: a simulation-based analysis

Abstract

This paper studies the effects of several tax reforms in an economy where taxes are partially evaded by means of undeclared work. To this purpose, we consider a two-sector dynamic general equilibrium model calibrated to Italy which explicitly accounts for underground production. We construct various tax reform scenarios, such as ex ante budget-neutral tax shifts from direct to indirect taxes, and tax cuts on labor and business financed by decreases of government spending. Our results indicate that neglecting the existence of the underground sector may lead to severely miscalculating the macroeconomic effects of tax reforms. Further, the dimension of the underground sector is permanently and considerably reduced by changes in the tax mix that diminish the labor tax wedge. Reductions of the business tax prove to be highly expansionary in the presence of a sizable informal sector.

Appendices

Appendix 1

1.1 Marginal costs of production in the intermediate good sector

This appendix derives the expression for firms’ marginal costs in order to show that they are equal for all producing firms. To see this, take the intermediate producers’ first-order conditions with respect to regular labor, underground labor, and capital, respectively Eqs. (12), (13), and (14)³⁸

$$\begin{aligned}&(1+\tau _{t}^{f,s})W_{t}^{m}=\frac{\alpha \hbox {MC}_{i,t}^{N}Y_{i,t}^{m}}{H_{i,t}^{m}}, \end{aligned}$$

(33)

$$\begin{aligned}&(1+ps\tau _{t}^{f,s})W_{t}^{u}=\frac{\alpha _{u}\hbox {MC}_{i,t}^{N}Y_{i,t}^{u}}{H_{i,t}^{u}}, \end{aligned}$$

(34)

$$\begin{aligned}&R_{t}^{k}=\hbox {MC}_{i,t}^{N}\left[ (1-\alpha )\frac{Y_{i,t}^{m}}{K_{i,t}} +(1-\alpha _{u})\frac{Y_{i,t}^{u}}{K_{i,t}}\right] , \end{aligned}$$

(35)

and use the first two to substitute for $\hbox {MC}_{i,t}^{N}Y_{i,t}^{m}$ and $\hbox {MC}_{i,t}^{N}Y_{i,t}^{u}$ into (14), to obtain

$$\begin{aligned} R_{t}^{k}=\frac{1-\alpha }{\alpha }(1+\tau _{t}^{f,s})W_{t}^{m}\frac{H_{i,t}^{m} }{K_{i,t}}+\frac{1-\alpha _{u}}{\alpha _{u}}(1+ps\tau _{t}^{f,s})W_{t}^{u} \frac{H_{i,t}^{u}}{K_{i,t}}. \end{aligned}$$

(36)

Now, use again Eqs. (12) and (13) after having substituted in them for $Y_{i,t}^{m}$ and $Y_{i,t}^{m}$ from Eqs. (7) and (8), respectively, and rearrange them as to have expressions for $\frac{H_{i,t}^{m}}{K_{i,t}}$ and $\frac{H_{i,t}^{u}}{K_{i,t}}$. By substituting these two ratios into (36), we obtain

$$\begin{aligned} R_{t}^{k}= & {} \frac{1-\alpha }{\alpha }\left( \alpha A^{m}\right) ^{\alpha -1}\left( \hbox {MC}_{i,t}^{N}\right) ^{\alpha -1}\left[ (1+\tau _{t}^{f,s})W_{t} ^{m}\right] ^{\frac{\alpha }{\alpha -1}}\nonumber \\&+\frac{1-\alpha _{u}}{\alpha _{u}}\left( \alpha _{u}A^{u}\right) ^{\alpha _{u}-1}\left( \hbox {MC}_{i,t}^{N}\right) ^{\alpha _{u}-1}\left[ (1+ps\tau _{t}^{f,s})W_{t}^{u}\right] ^{\frac{\alpha _{u}}{\alpha _{u}-1}}, \end{aligned}$$

(37)

which solved for $\hbox {MC}_{i,t}^{N}$ shows how the latter does not depend on firm specific variables, that is, it is equal for all firms.

1.2 Complete set of equilibrium conditions

• $P_{t}^{F}Y_{t}^{F}=P_{t}Y_{t}^{H}+S_{t}P_{t}^{M}M_{t},$ equilibrium condition in the final good sector

• $Y_{t}^{H}=(1-\alpha _{M})\left( \frac{P_{t}}{P_{t}^{F}}\right) ^{-\sigma _{M}}Y_{t}^{F},$ demand for domestic intermediate goods

• $M_{t}=\alpha _{M}\left( \frac{S_{t}P_{t}^{M}}{P_{t}^{F}}\right) ^{-\sigma _{M}}Y_{t}^{F},$ demand for foreign intermediate goods (imports)

• $Y_{t}=Y_{t}^{H}+X_{t},$ equilibrium condition in the intermediate good sector good sector

• $X_{t}=\alpha _{X}\left( \frac{P_{t}}{S_{t}P_{t}^{F^{*}}}\right) ^{-\sigma _{X}}Y_{t}^{F^{*}},$ foreign demand for domestic intermediate goods (exports)

• $Y_{t}^{m}=\Delta _{t}^{-1}A^{m}\left( H_{t}^{m}\right) ^{\alpha } K_{t}^{1-\alpha },$ legal production of intermediate goods

• $Y_{t}^{u}=\Delta _{t}^{-1}A^{u}\left( H_{t}^{u}\right) _{u}^{\alpha }K_{t}^{1-\alpha _{u}},$ underground production of intermediate goods

• $Y_{t}=Y_{t}^{m}+Y_{t}^{u},$ total production of intermediate goods

• $(1+\tau _{t}^{f,s})W_{t}^{m}=\frac{\alpha \hbox {MC}_{t}^{N}Y_{t}^{m}}{H_{t} ^{m}},$ demand for legal labor

• $(1+ps\tau _{t}^{f,s})W_{t}^{u}=\frac{\alpha _{u}\hbox {MC}_{t}^{N}Y_{t}^{u} }{H_{t}^{u}},$ demand for illegal labor

• $R_{t}^{k}=\hbox {MC}_{t}^{N}\left[ (1-\alpha )\frac{Y_{t}^{m}}{K_{t}} +(1-\alpha _{u})\frac{Y_{t}^{u}}{K_{t}}\right] ,$ demand for capital

• $\widehat{p}_{t}=\frac{\theta }{\theta -1}\frac{E_{t}\sum _{j=0}^{\infty }\psi ^{j}Q_{t,t+j}^{R}\hbox {MC}_{i,t+j}\left( \frac{P_{t+j}}{P_{t}}\right) ^{\theta _{Y}}Y_{t+j}}{E_{t}\sum _{j=0}^{\infty }\psi ^{j}Q_{t,t+j}^{R}\left[ (1-\tau _{t+j}^{y})+\tau _{t+j}^{y}(1-ps)\frac{Y_{i,t}^{u}}{Y_{i,t}}\right] \left( \frac{P_{t+j}}{P_{t}}\right) ^{\theta _{Y}-1}Y_{t+j}},$ optimal price setting condition (where $Q_{t,t+j}^{R}=\beta \frac{\lambda _{t+j}}{\lambda _{t} }$)

• $1=\psi \varPi _{t}^{\theta -1}+\left( 1-\psi \right) \widehat{p} _{t}^{1-\theta },$ PPI inflation

• $\Delta _{t}=\left( 1-\psi \right) ^{-\theta }+\psi \varPi _{t}^{\theta } \Delta _{t-1},$ price dispersion

• $\lambda _{t}=\frac{\left( C_{t}-\eta \bar{C}_{t-1}\right) ^{-\sigma } }{1+\tau _{t}^{c}}\frac{P_{t}}{P_{t}^{F}},$ first-order condition of the representative household with respect to consumption

• $\,H_{t}^{m}+H_{t}^{u}=\lambda _{t}^{\frac{1}{\xi }}\left[ \frac{(1-\tau _{t}^{h}-\tau _{t}^{h,s})W_{t}^{m}/P_{t}}{\varGamma _{0}}\right] ^{\frac{1}{\xi }},$ total labor supply

• ${H_{t}^{u}\!=\! {\left\{ \begin{array}{ll} \lambda _{t}{}^{\frac{1}{\varphi }}\left( \frac{\left[ 1-ps(\tau _{t}^{h} +\tau _{t}^{h,s})\right] \frac{W_{t}^{u}}{P_{t}}-(1-\tau _{t}^{h}-\tau _{t}^{h,s})\frac{W_{t}^{m}}{P_{t}}}{\varGamma _{1}}\right) ^{\frac{1}{\varphi } }\!\!, &{} \text {if} \; \left[ 1-ps(\tau _{t}^{h}+\tau _{t}^{h,s})\right] \frac{W_{t}^{u}}{P_{t}}\\ &{}\quad \quad \ge (1-\tau _{t}^{h}-\tau _{t}^{s,h})\frac{W_{t}^{m} }{P_{t}},\\ 0, &{} \text {otherwise,} \end{array}\right. }}$ supply of illegal labor

• $Q_{t}=\beta E_{t}\frac{\lambda _{t+1}}{\lambda _{t}}\frac{P_{t}^{F} }{P_{t+1}^{F}},$ Euler equation (nominal risk-free asset)

• $K_{t+1}=(1-\delta )K_{t}+\left[ 1-S\left( \frac{I_{t}}{I_{t-1} }\right) \right] I_{t}$ with $S\left( \frac{I_{t}}{I_{t-1}}\right) =\frac{\phi _{I}}{2}\left( \frac{I_{t}}{I_{t-1}}-1\right) ^{2}$, accumulation of physical capital

• $q_{t}=\beta E_{t}\frac{\lambda _{t+1}}{\lambda _{t}}\left[ (1-\tau _{t+1}^{k})\frac{R_{t+1}^{k}}{P_{t+1}}+q_{t+1}(1-\delta )\right] ,$ first-order condition of the representative household with respect to capital where $q_{t}$ is the Tobin’s q

• $1=q_{t}\frac{P_{t}}{P_{t}^{F}}\left[ 1-\phi _{I}\left( \frac{I_{t} }{I_{t-1}}-1\right) \frac{I_{t}}{I_{t-1}}-\frac{\phi _{I}}{2}\left( \frac{I_{t}}{I_{t-1}}-1\right) ^{2}\right] +\beta E_{t}q_{t+1}\frac{\lambda _{t+1}}{\lambda _{t}}\frac{P_{t}}{P_{t}^{F}}\phi _{I}\left( \frac{I_{t+1}}{I_{t}}-1\right) \left( \frac{I_{t+1}}{I_{t}}\right) ^{2},$ first-order condition of the representative household with respect to investment

• $\frac{\lambda _{t}S_{t}}{P_{t}}=\beta \frac{E_{t}\lambda _{t+1}S_{t+1} }{P_{t+1}}R_{t}^{*},$ Euler equation on foreign asset

• $R_{t}^{-1}B_{t+1}=B_{t}+P_{t}^{F}G_{t}-T_{t},$ public debt

• $T_{t}=(\tau _{t}^{h}+\tau _{t}^{h,s}+\tau _{t}^{f,s})W_{t}^{m}H_{t} ^{m}+ps(\tau _{t}^{h}+\tau _{t}^{h,s}+\tau _{t}^{f,s})W_{t}^{u}H_{t}^{u}+\tau _{t}^{c}P_{t}^{Y}C_{t}+\tau _{t}^{y}P_{t}\left( Y_{t}^{m}+psY_{t}^{u}\right) +T_{t}^{ls},$ total tax revenues

• $S_{t}F_{t+1}=R_{t}^{*}S_{t}F_{t}+P_{t}X_{t}-S_{t}P_{t}^{M}M_{t},$ foreign asset equation

• $R_{t}^{*}=\tilde{R}_{t}^{*}-\varphi ^{F}(e^{f_{t}-f}-1),$ risk-adjusted interest rate on foreign asset

• $Y_{t}=\frac{P_{t}^{F}}{P_{t}}C_{t}+\frac{P_{t}^{F}}{P_{t}}G_{t} +\frac{P_{t}^{F}}{P_{t}}I_{t}+X_{t}-\frac{S_{t}P_{t}^{M}}{P_{t}}M_{t},$ resource constraint of the economy

• $\hbox {ToT}_{t}=\frac{P_{t}}{P_{t}^{M}}=\frac{P_{t}}{S_{t}P_{t}^{*}}$, terms of trade

The (average) markup is given by $P_{t}/\hbox {MC}_{t}^{N}.$ Trade balance as a fraction of output is measured as $\left( X_{t}-\frac{S_{t}P_{t}^{M}}{P_{t} }M_{t}\right) /Y_{t}.$

The model is solved under the two following monetary and fiscal policy hypotheses:

• $S_{t}=S,$

• $T_{t}^{ls}$ adjusts so that $B_{t}/P_{t}$ is constant over time.

1.3 Welfare computation

This appendix describes the welfare measure we use to evaluate the effects of the envisaged tax reform scenarios. Let a and b be two alternative generic policies that can be implemented by the government. Then, the present discounted value of the utility flow under policy a is:

$$\begin{aligned} V_{T}^{a}=\sum _{t=1}^{T}\beta ^{t}U(C_{t}^{a},H_{t}^{m,a},H_{t}^{u,a}), \end{aligned}$$

(38)

where $C_{t}^{a}$, $H_{t}^{m,a}$, and $H_{t}^{u,a}$ respectively denote consumption, regular hours, and irregular hours under policy a, and T is the time horizon we are interested in evaluating the welfare effects of the reform. Similarly, the present discounted value of the utility flow under policy b is:

$$\begin{aligned} V_{T}^{b}=\sum _{t=1}^{T}\beta ^{t}U(C_{t}^{b},H_{t}^{m,b},H_{t}^{u,b}), \end{aligned}$$

(39)

where clearly, $C_{t}^{b}$, $H_{t}^{m,b}$, and $H_{t}^{u,b}$, respectively, denote consumption, regular hours, and irregular hours under policy b. The welfare cost of adopting policy a instead of policy b is defined as the constant fraction of consumption, $\omega$, that individuals have to give up under policy b in order to be indifferent between the two policies. Formally, $\omega$ represents the solution to the following identity:

$$\begin{aligned} V_{T}^{a}=\sum _{t=1}^{T}\beta ^{t}U\left( (1-\omega )C_{t}^{b},H_{t} ^{m,b},H_{t}^{u,b}\right) . \end{aligned}$$

(40)

If computed in this way, $\omega$ allows to capture the transitional welfare effects of different fiscal reforms. Another broadly used measure of welfare only looks at the steady state effects of policy reforms. Similarly to (40), the steady state welfare cost $\omega _{ss}$ solves

$$\begin{aligned} U\left( C^{a},H^{m,a},H^{u,a}\right) =U\left( (1-\omega _{ss})C^{b} ,H^{m,b},H^{u,b}\right) . \end{aligned}$$

(41)

The distinction between transitional and steady state welfare effects is important since it might be the case that a policy is welfare improving in the steady state, whereas it generates negative effects in transition (and vice versa).

Appendix 2

In what follows we report the transition dynamics and the steady-state effects of marginal changes in the tax rates and in public expenditure. We consider each policy intervention in isolation. Of course in this case the policy experiments are not fully comparable, since the tax bases are different. As in the case of revenue-neutral policy combinations, we observe that the stronger effects on output are recorded in case of a small underground sector. The terms of trade effect operates, as in the combined experiments, by diminishing the differences across economies in the short-run (Figs. 6, 7, 8, 9, 10; Table 11).

Fig. 6

1 p.p. cut in the business tax rate

Fig. 7

1 p.p. cut in the labor income tax rate

Fig. 8

1 p.p. cut in the employers’ SSC tax rate

Fig. 9

1 p.p. increase in the consumption tax rate

Fig. 10

1 p.p. cut in public spending

Table 11 Non compensated tax changes—steady state results

Table 12 0.5% of output cut in the business tax base financed by an increase in the consumption tax

Appendix 3

In this appendix we show the effects of two additional fiscal experiments, namely (1) 0.5% of output reduction of the business tax base achieved by introducing a partial deductibility of labor cost and financed by an increase in the consumption tax (Table 12); (2) 0.5% of output cut in SSC bearing on firms financed by an equal size reduction of public spending (Table 13). For each variable and dimension of the underground sector we report a vector of three elements, where the first two elements refer to 1 and 5 years, while the third element refers to the impact of the reform on the long-run (steady-state) levels of economic activity.

Table 13 0.5% of output cut in SSC financed by public spending reduction

Table 14 Tax reform scenarios—no frictions

Table 15 Tax reform scenarios—no nominal rigidities

Table 16 Tax reform scenarios—habit persistence

Appendix 4

In this appendix we explore the role of frictions in shaping the response of the economy. For each variable, scenario and dimension of the underground sector, we report a vector of three elements, where the first two elements refer to 1 and 5 years, while the third element refers to the impact of the reform on the long-run (steady-state) levels of economic activity.

In Table 14 all the fiscal experiments are conducted by removing the adjustment costs on investments, consumption habit and nominal rigidities. In the absence of any frictions all variables adjust immediately to the new fiscal system. We observe major reactions of consumption and investment, as a result of the absence of habit and of real adjustment costs, while the markup reaches immediately its long run level since prices are fully flexible and price setters can immediately adjust them so as to maximize current profits.

Table 15 shows the impact of the tax reforms in an economy featuring real frictions but not nominal rigidities, while Table 16 presents the results for an economy displaying only habit formation, but neither adjustment cost on investments, nor nominal frictions. Under flexible prices, but with real frictions on investment and consumption, the 1 year response of the economy to the fiscal reforms envisaging a cut of the business tax is minor, since the average markup does not overshoot its long run level, as observed in the benchmark case. On the contrary, in $S_{2}$, $S_{3}$ and $S_{5}$ the markup does not jump up excessively, therefore the initial impact on output is higher than in the benchmark case. Under the assumption that the only friction characterizing the economy is given by habit persistence, as expected, investments are shown to be more reactive in the short-run than in the benchmark case.